This invention relates to an adaptive digital filter capable of generating an arbitrary transfer function. In particular, it relates to an adaptive digital filter having a fast rate of convergence, suitable for use in a device such as an echo canceler.
Recent rapid progress in digital signal-processing technology has created great interest in adaptive digital filters due to their wide range of applications. Typical of these applications is system identification, which is a process of estimating an unknown system characteristic from input and output data.
Means for the identification of an unknown system by use of an adaptive digital filter are shown in schematic form in FIG. 1. These means comprise a signal input terminal 41, an error output terminal 42, an unknown system 43, an adaptive digital filter (ADF) 44, and an adder 45. In the figure, x(k) is the input to the unknown system 43 and the adaptive digital filter 44 at time k, y(k) is the output from the unknown system 43 at time k, y(k) is the output from the adaptive digital filter 44 at time k, e(k) is the estimation error at time k, H(z) is the transfer function of the unknown system, and H(z) is the transfer function of the adaptive digital filter 44. In the configuration shown, if the evaluation function is J=e(k).sup.2, then when J=O the adaptive digital filter 44 is regarded as correctly estimating the characteristic of the unknown system 43.
A specific type of device using an adaptive digital filter like the one described above is an echo canceler. Echo cancelers are used, for example, in teleconferencing systems, for which there has been a recently growing demand. FIG. 2 is a schematic diagram of a teleconferencing system employing an echo canceler. This system comprises a pair of microphones 51-1 and 51-2, a pair of loudspeakers 52-1 and 52-2, a pair of echo cancelers 53-1 and 53-2 having respective adaptive digital filters 55-1 and 55-2, and a pair of transmission lines 54-1 and 54-2, and 55-2, and has a pair of acoustically coupled paths 56-1 and 56-2. In most teleconferencing systems the loudspeaker and microphone shown in FIG. 2 are integrated into a single unit called a voice terminal. This gives rise to an acoustic coupling between the loudspeaker and the microphone: the signal output from the loudspeaker is coupled into the microphone and greatly degrades the quality of the voice transmission. In FIG. 2 there are acoustic coupling paths, labeled 56-1 and 56-2, between the loudspeaker 52-1 and the microphone 51-1, and between the loudspeaker 52-2 and the microphone 51-2, but the echo cancelers 53-1 and 53-2 act to reduce the signal coupled from the loudspeaker into the microphone.
FIG. 3 shows the type of adaptive digital filter used in such an echo canceler in the prior art. (See the Proceedings of the 1985 Symposium on Information Systems of the Institute of Electronics and Communication Engineers of Japan, No. 366, pp. 2-107.) The adaptive digital filter in FIG. 3 comprises M basic sections, where M is a positive integer. Each basic section except the M-th comprises a second-order recursive digital filter F1 (having unit delay elements 62-1 and 63-1), a second-order non-recursive digital filter F2, and a first-order non-recursive digital filter F3. The zeros of the second-order non-recursive digital filter F2 are mirror images of the poles of the second-order recursive digital filter with respect to the unit circle. The M-th basic section comprises a second-order recursive digital filter and a first-order non-recursive digital filter. The first outputs (OUT1) of the M basic sections are connected to the inputs of an adder 64, the output of which is the output of the adaptive digital filter. The second outputs (OUT2) of the first through M-1-th basic sections are connected to the inputs of the next higher basic section. The input of the first basic section is the input to the adaptive digital filter.
In an adaptive digital filter configured as above, let .phi..sub.1 (k), .phi..sub.1 (k-1), .phi..sub.2 (k), .phi..sub.2 (k-1), . . . , .phi..sub.M (k), .phi..sub.M (k-1), be the input signals to the variable-coefficient scalers 60-1, 61-1, 60-2, 61-2, . . . , 60-M, 61-M, the variable coefficients of which are p.sub.1, q.sub.1, p.sub.2, q.sub.2 . . . , p.sub.M, q.sub.M. Then the following relationships hold: ##EQU1## Where i=1, 2, . . . , M; l=1, 2, . . . , M; and i.noteq.l. The overbar.sup.-- denotes the result of an averaging operation at time k. The above equations indicate that the inputs to the variable-coefficient scalers of ADF-i and ADF-l are orthogonal.
In an adaptive digital filter employing the prior art as shown in FIG. 3, however, the average value of the product of the input signal .phi..sub.i (k) of the variable-coefficient scaler 60-i and the input signal .phi..sub.i (k-1) of the variable-coefficient scaler 61-i in the i-th basic section is not 0: EQU .phi..sub.i (k).phi..sub.i (k-1).noteq.0(i=1, 2, . . . , M)(2)
Also, the mean square values .phi..sub.1.sup.2 (k), .phi..sub.2.sup.2 (k), . . . , .phi..sub.M.sup.2 (k) of the input signals .phi..sub.1 (k), .phi..sub.2 (k), . . . , .phi..sub.M (k) are not equals: EQU .phi..sub.i.sup.2 (k)=.phi..sub.l.sup.2 (k)(i.noteq.l) (3)
As a result, the convergence rate of the variable coefficients p.sub.1, q.sub.1, p.sub.2, q.sub.2, . . . , p.sub.M, q.sub.M is slow.